Some New Results for Linear Transformations on Euclidean Jordan Algebras
Jiyuan Tao, Theodore E. Simos, George Psihoyios, Ch. Tsitouras · AIP conference proceedings · 2009
Generalizing the w−P property of a matrix, Tao [Some w−P properties for linear transformations on Euclidean Jordan algebras, to appear in Pacific J. Optimization] recently introduced and studied the w−P and the w‐uniqueness properties for linear transformations defined on Euclidean Jordan algebras. In this paper, we study further to these properties. In particular, we specialize them to the space Sn of all n×n real symmetric matrices and the space Hn of all n n complex Hermitian matrices for Lyapunov and Stein transformations. We also present a sufficient condition for the w‐uniqueness property on Sn. In addition, we give a characterization of the w−P and the column sufficiency properties for a matrix‐induced transformation on Euclidean Jordan algebras.